Case Studies
Your
contributions
to this department are invited! We're looking for short descriptions of
interesting examples and/or fruitful applications of the algorithms or
other
ideas in A=B.
 Proof
of an identity of FeiginStoyanovsky shows the proof of a
complicated qidentity, handled by qEKHAD in routine fashion, in
response to a request from those who conjectured it and needed it for
other purposes. (An Acrobat file)
 How
to do MONTHLY problems
with your computer (by Nemes, Petkovsek, Wilf and
Zeilberger) appeared
in the American Math. Monthly. It has a large number of examples of the
methods in action. (An Acrobat file)
 A
Mathematica notebook that exhibits all of the examples that are in
the MONTHLY paper above.
If Mathematica 3.0 is available to you, then with this notebook you
will be able to see and to follow in detail exactly how each of the MONTHLY problems was done by
computer. If also you have downloaded the four
basic packages (qzeil.m, zb.m, gosper.m, hyper.m) then you will be
able not only to follow the solutions of these problems, but also to
run them for yourself and see the answers happen.
 An
identity of J. S. Lomont and John Brillhart has a proof of an
identity that looked difficult because it has no less than 7 binomial
coefficients in it, but turned out to be an exercise in Gosper's
algorithm.
 The
Filbert Matrix has entries that are reciprocals of Fibonacci
numbers. Many interesting properties of the matrix have been found by
Tom Richardson, some with the aid of the methods from "A=B".
 Here is a paper of Ivan Selesnick
in which the methods of "A=B" are used to find a recurrence that has
applications to lowpass filters.

This is a proof of an identity of Gasqui and Goldschmidt, which they encountered during a study of
Radon transforms.
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